Network Externality and Strategic Investment in the Banking ...

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Network Externality and Strategic Investment in the Banking ...

  1. 1. Network Externality, Dynamic Competition and Social Welfare in the Banking Industry- A Real Options Approach T.S. Johnson Cheng † , I-Ming Jiang ∗ , Shih-Cheng Lee ‡ and Banghan Chiu § Abstract By using the Real Options Approach, this paper concludes that banking industries have to maintain the flexibility of decision-making when facing uncertain market demand. In addition, when the network externality exists, although there are sufficient incentives to attract banking industries to invest in electronic commerce platform, the increasing uncertainty of network externality will have the optimal investment timing deferred, implying leaders must have investment strategies adjusted for the first-mover advantage in response to potential threats from opponents entering the market. Finally, our sensitivity analysis indicates that competition does not necessarily improve social welfare due to market uncertainty and network externality. Keywords:Real Options Approach, Network Externality, Banking Industry, Strategic Investment, Social Welfare † Associate Professor, Department of international Business, Soochow University, No. 56, Kueiyang Street, Section 1, Taipei, Taiwan. Email: johnson@scu.edu.tw ∗ Assistant Professor, Department of Finance, Yuan Ze University, No. 135, Far-East Rd., Chung-Li, Taoyuan, Taiwan. Email: jiangfinance@saturn.yzu.edu.tw ‡ Associate Professor, Department of Finance, Yuan Ze University, No. 135, Far-East Rd., Chung-Li, Taoyuan, Taiwan. Email: sclee@saturn.yzu.edu.tw § Associate Professor, Department of Finance, Yuan Ze University, No. 135, Far-East Rd., Chung-Li, Taoyuan, Taiwan. Email: sclee@saturn.yzu.edu.tw
  2. 2. 1. Introduction Shy (2001) indicates that the network industry includes telecommunications, radio broadcasting and television, information and communications technology (ICT), aviation industry, and banking industry. According to the OECD 2008 report, among all above industries, the banking industry contributes 6%~7% value-added shares relative to the total economy in G7 countries. Thus, compared to other network industries only contributing 1%~3%, the banking industry deserves more attention. The network economics is used to mainly discuss pricing strategies, compatible standards and market competition; however, the issue of network externality 4 has drawn great interests nowadays. For example, in the banking industry, the establishment of Automatic Teller Machine (ATM) has become an un-neglected job because of its great possibility of network externality, although it requires lots of capital input. According to the estimation of Kivel and Rubin (1996), the server of online bank costs US$10,000 and the network assess costs around US$200,000~US$4 billion, depending on the scale 4 Rohlfs (1974) pointed out that the network externality in the telecommunications industry is with higher telecommunication value when there are more linking points, that is, the necessity of telecommunication is reinforced. In other words, people prefer to majority communications due to a herding psychology; therefore, a greater network, the more importance of joining the network. Katz and Shapiro (1985) defined it in the sense of industrial economy as: “the utility to the consumers is with higher value along with the increase of network users in number.” Varian and Shapiro (1999) defined it as: “if the price that an individual is willing to pay for the network system is relevant to the number of network users or targets, the network externality is in existence”. 1
  3. 3. of operation. Besides, Forrester Research Center estimates the construction and maintenance of a trade network costs around US$5 million~US$23 million (Bank Network News, June 23, 1998). Apparently, the scale of business and network externality do affect the performance of banks. The information technology system of ATM and Internet Bank has high development cost and high customer service expense; also, the feature of scale economies, that is, the more users the lower marginal cost of transmission service. Therefore, the profits of banks rely on the number of users or the market share. The effort of developing and maintaining customers is important to banks; therefore, network externality plays an important role in this industry. The impact of network externality on the profits of banks is mostly on the ATM, branch setup, and the Internet use of credit cards. Saloner and Shepard (1995) concluded that banks would adopt ATM sooner along with the increase of branches and customers in number. Osterberg and Thomson (1998) pointed out that the network-dependent value would be generated and the profits of banks would be improved if the credit card business and the number of merchants accepting the credit card business increase. Under the circumstance, credit card market is with significant network externality effect 5 . Ishii (2005) argued that the incompatibility of ATM caused 5 The Electronic Payment Systems (EPS) of PC banks faces the situation stated by Osterberg and Thomson (1998), and Stavins (1997) confirmed the existence of network effect, that is, the more Internet 2
  4. 4. surcharge and with a significant impact on the deposit business of banks 6 . The empirical research of Nickerson and Sullivan (2006) indicated that the profits distribution of banks was affected by expected profits and variation. The scale of banks (market share) affects the expected profits. When the variation is given, large banks will become Internet Banks first. According to the empirical research of Berger and Dick (2007), domestic banks that had entered the market earlier did occupy 15% more market share. The First Mover Advantage (FMA) is resulted from the network effect among branches 7 . The establishment of information system takes a great deal of sunk cost, and the future demand of customers cannot be expected precisely; therefore, the Net Present Value (NPV) method for evaluating a capital investment cannot have the investment timing and flexibility assessed, and may have the opportunity cost of investment plan underestimated. According to the Real Options Approach, an investment plan has three features: uncertain return, irreversible cost and flexible investment timing (McDonald and Siegel, 1986; Dixit and Pindyck, 1994). By considering these three factors, the Real Options Approach is able to have the disadvantages of NPV amended. Therefore, banks users, the higher benefit for each participant. 6 There is usually no surcharge for using the ATM of the same bank; however, service charge for inter-bank withdrawal and account transfer is inevitable. 7 The empirical study of Grzelonska (2005) shows the positive relationship between the network benefit of the branch (adjacency) and the deposits amount of banks. 3
  5. 5. must maintain flexible decision-making while facing uncertain electronic commerce and marketing development in order to have the management strategies amended and the optimal investment opportunities controlled. Miranda (2001) used the Real Options Approach to consider the optimal investment decisions for equipment expansion of monopoly banks under the network externality. The result shows that when there is a positive network effect, the increase of users in number will cause the options value to go up. Therefore, firms own the growth options for operation expansion once future demand increases. Mason and Weeds (2000) discussed the best timing for duopoly firms to introduce new technology if the technology was with network externality and preemption. The most Real Options Approach literature believes that network externality effect must be positive and constant whereas Prasad and Harker (2000) argued that network externality effect could be a positive or a negative 8 , and could be a random variable that was in conformity with Geometric Brownian Motion (GBM). This study is utilizing the Real Options Approach to analyze the investment strategies of Internet Banks under the random network effect by taking into account the following factors: (1) irreversible construction cost, (2) future growth, (3) uncertain network effect, and (4) the intensity of network effect. Besides, we also compute the 8 Kennickell and Kwast (1997) stated that in terms of Internet bank; only 33% users based their decision on friends and the relevant information. Thus, network is not necessarily with a positive effect resulted. 4
  6. 6. social welfare under different parameter specifications. This paper is organized as follows. Section 2 defines the Cournot-Nash equilibrium output and investment profits under the existence of network externality. Section 3 discusses the optimal investment timing under the banks’ strategic interaction. The demand threshold and equilibrium entry strategy is described in Section 4. Calculation of social welfare and the sensitivity analysis are shown in Section 5, and Section 6 concludes this study. 2. Equilibrium Output, Network Effect, and Bank’s Value Assume there are two banks in the market, and the inverse market demand of banking service is a linear function: p ( q, θ ) = θ − q (1) where q stands for the total market demand (Total output q = q1 + q2 , q1 and q2 indicates the quantity provided by Bank 1 and Bank 2), θ stands for the stochastic demand shift parameter. As suggested by Prasad and Harker (2000), network externality could be a random variable in conformity with Geometric Brownian Motion (GBM), thus: dθ = α dt + σ dz θ (2) In Equation (2), α is the instantaneous average change per time unit of θ. σ is the standard deviation of the instantaneous change per time unit. dz is the increase of 5
  7. 7. Wiener process, and the initial time is θ 0 . If the demand is with network externality, we follow Lin and Kulatilaka (2006) 9 model to have the inverse demand curve of Internet banking service rewritten as follows: p (q, q e , θ ) = θ + v( q e ) − q (3) e e where q is the network scale expected by the network users. v(q ) stands for the value that network users are willing to pay for the additional network service provided, and it increases with the network scale. According to Metcalfe’s law, the total value of network service is a constant ratio of the square of network users. q ⋅ v(q e ) = ζ q 2 (4) Therefore, for each consumer, Internet banking service value could be expressed as follows: v(q e ) = ζ q (5) Lin and Kulatilaka (2006) defined ζ as the intension of network effect and its value falls in [0,1) 10 . For simplification, our model assumes that banks are without variable costs; therefore, the profits flow of banks i ( i = 1, 2 ) in stage 2 at time t is: 9 Lin and Kulatilaka (2006) assumed that the exogenous expectation and the network effect of consumers to be homogeneous. 10 If ζ = 0, demand function returns to Equation (1). In order to maintain the negative slope of the demand curve, ζ <1 is defined. 6
  8. 8. π i (qi ) = pqi = [ (θ − q + ζ q )] qi (6) The Gross Project Value ( Vi ) of the investment and the NPVi of Bank i in stage 2 is defined as: NPVi = Vi − I (7) and I is the initial investment in stage 2. Since we assume there are two banks 1 and 2, under the Cournot-Nash competition, the reaction function of Bank 1 and Bank 2, and the optimal competitive equilibrium output are as follows: θ − (1 − ζ )q2 R1 ( q2 ) = 2 (1 − ζ ) (8a) and θ − (1 − ζ )q1 R2 ( q1 ) = 2 (1 − ζ ) (8b) and the Cournot-Nash competitive equilibrium solution is: θ q1∗c = q2 c = ∗ 3 (1 − ζ ) (8c) Therefore, under the duopoly, the profits flow π ic of Bank i ( i = 1, 2 ) equals to: θ2 π ic = 9 (1 − ζ ) (9) From Equation (9), we notice that the greater intensity of network effect ζ , the greater profits flow of duopoly banks. Under the Cournot-Nash competitive equilibrium, 7
  9. 9. the project value Vic of Bank i ( i = 1, 2 ) equals to 11 : θ2 Vic = 9δ (1 − ζ ) (10) In Equation (10); δ = λ − 2α − σ 2 > 0 λ is the constant equilibrium risk-adjusted discount rate after risk adjustment 12 ;On the other hand, under a monopoly, the project value Vim of Bank i equals to: θ2 Vim = 4δ (1 − ζ ) (11) Comparing Equation (10) and Equation (11), it shows that the result is clearly similar to the traditional Cournot-Nash competitive equilibrium solution in literature except for the inclusion of the intensity of network effect. We also can know that the project value will be higher if the intensity of network effect ( ζ ↑) and the parameter of the uncertainty of network externality are higher ( σ ↑ or δ ↓ ). 2 In this section, we have shown that greater the intensity of network effect and greater the uncertainty of network externality will help banks acquire greater profits comparing to the non-Internet bank marketing. Therefore, banks should invest to 11 In general case, the gross project value ( Vi ) of the investment and the NPVi of Bank i in stage 2 could be derived as follows: πi Vi =E ∫ π i (θ )dt = , ( n + 1) ⋅ δ ⋅ (1 − ς ) 2 where n is the number of banks, which is determined by the market competition structure. For example, when firm is monopoly: n =1 ; when firm is duopoly: n =2 and equation (10) and (11) can be obtained. 12 According to the Capital Asset Pricing Model (CAPM), μ should reflect the asset’s systematic (non-diversifiable) risk, that is, μ = r + φρ xmσ , where ρ xm is the correlation coefficient of portfolio x with market portfolio, and φ is the market price of risk. 8
  10. 10. construct Internet bank service platform and promote Internet bank marketing before competitors in order to improve industrial profitability significantly. 3. Bank’s Entry Strategy In this section, we try to understand how the leading banks (the existing banks) respond to the investment strategies of competitors attempting to invest and construct network marketing platform for competition. We consider bank’s entry strategy in accordance with the two-stage model of Joaquin and Butler (2000) here. The first mover in stage 1 initially obtains the monopoly profits. Competitors will have incentives to enter the market due to the excessive profits in stage 1. In stage 2, the first mover has to share the monopoly profits with the competitors and with lower profits expected; therefore, it is necessary to have the strategy adjusted in response to the market entry of competitors. Followers (potential competitors) entering market to share the monopoly profits of the existing banks in stage 2 will be discussed first in Section 3.1. 3.1 Follower’s Decision-Making Assume before the investment, the value of the investment plan of the following Bank 2 is V0F (θ ) ; besides, the instantaneous equilibrium return of the following banks 9
  11. 11. before entering the market is: rV0F (θ )dt = E[dV0F (θ )] (12) where r is the risk-free interest rate. The economic implication of Equation (12) is that the total expected return of an investment project equals to the expected return of capital valuation at any time interval. According to Ito’s Lemma, the expected capital gain E[dF (V (θ ))] can be rewritten as follows: 1 E[dF (V (θ ))] = σ 2θ 2V0F '' (θ )dt + α ⋅θV0F ' (θ )dt (13) 2 We then can derive Bellman equation by applying Equation (13) to Equation (12): 1 2 2 F '' θ2 σ θ V0 (θ ) + αθV0F ' (θ ) + = rV0F (θ ) (14) 2 9 (1 − ζ ) where the beginning investment value V0F must fulfill the boundary conditions: lim V0F (θ ) = 0 (15) θ → 0+ Equation (14) illustrates that follower’s investment after entering the market must satisfy the differentials equation in accordance with the potential investment uncertainty, the network effect intensity and network eternality. Equation (15) indicates that there is no opportunity for arbitrage; in other words, the derived options value of an investment with zero value is zero. If we consider the solution of Equation (14) of the following bank’s investment is polynomial and is specified as follows: 10
  12. 12. ⎡ θ2 ⎤ V0F (θ ) = B1 ⋅ θ β1 + B2 ⋅ θ β 2 + ⎢ ⎥ (16) ⎣ 9δ (1 − ζ ) ⎦ in which, B1 and B2 are constants and determined endogenously. β1 and β 2 are the solutions to the quadratic equations: 1 2 σ β ( β − 1) + αβ − r = 0 (17) 2 that is, 1 1 α ⎧ α 1⎤ ⎫2 2 ⎪⎡ 2r ⎪ β1 = − 2 + ⎨ ⎢ 2 − ⎥ + 2 ⎬ > 1 (18a) 2 σ ⎪⎣σ ⎩ 2⎦ σ ⎪ ⎭ and 1 1 α ⎧ α 1⎤ ⎫2 2 ⎪⎡ 2r ⎪ β2 = − 2 − ⎨⎢ 2 − ⎥ + 2 ⎬ < 0 (18b) 2 σ ⎪⎣σ ⎩ 2⎦ σ ⎪ ⎭ The duopoly banks will maintain the same output level if there is further entry difficulty for other following banks. Therefore, Equation (16) explains the value of Bank 2 with an assumption that Bank 1 has investment made already. In other words, for Bank 2, B1 = B2 = 0 ; therefore, under duopoly, the fundamental value of the following bank’s investment is: θ2 V0F (θ ) = (19) 9δ (1 − ζ ) If we assume that the following bank implements the investment plan and the fixed costs equals I. The net present value of the investment plan can be obtained as follows: NPVF (θ ) = V0F (θ ) − I (20) If the following bank decides to have the investment plan executed at the time 11
  13. 13. when θ is greater than the demand threshold θ F ( θ ≥ θ F ), the value of waiting ∗ * equals to the net present value of the investment plan enforced by the following banks when θ ≥ θ F 13 . * NPVF (θ F ;θ ) = Eθ ⎡{V0F (θ F ) − I } e − rT ⎤ * ⎣ * ⎦ (21) where Eθ is the risk-neutral expectation operator of the initial demand θ . Therefore, when the demand threshold is θ ≥ θ F , the options value of investment * for the following bank today is NPVF (θ F ;θ ) . By substituting Equation (19) in * Equation (21), we then derive the net present value: β1 ⎡ θF 2 * ⎤⎛ θ ⎞ NPVF (θ ;θ ) = ⎢* − I⎥⎜ * ⎟ (22) ⎣ 9δ (1 − ζ ) ⎦ ⎝ θ F ⎠ F Thus, when the investment is uncertain, the cost is irreversible, and it is able to await ( θ ≥ θ F ), we are able to derive the optimal entry threshold for the following bank * with maximized waiting value from the First order condition of Equation (22): 1 1 ⎧ β ⎫2 ⎧ β ⎫2 θ F = 3 ⎨ 1 I δ (1 − ζ ) ⎬ = 3 ⎨ 1 I ⎡( λ − 2α − σ 2 ) (1 − ζ ) ⎤ ⎬ ∗ ⎣ ⎦ (23a) ⎩ β1 − 2 ⎭ ⎩ β1 − 2 ⎭ 13 We defined τ as the first passage time of θ exceeding the demand threshold θ i∗ ( i = F, L ) when the initial demand is θ 0 at time 0. It also can be expressed mathematically as: τ ≡ τ (θ i* ; θ ) = in f ( t ≥ 0 : θ t ≥ θ i* ) E ⎡e − rτ ⎤ , i = F , L . Besides, it is necessary to have the θ ⎣ ⎦ calculated for solving the deferral value of an investment; and we can obtain it from Dixit and Pindyck (1994, pp. β1 − rτ ⎛θ ⎞ Eθ ⎡ e ⎣ ⎤ =⎜ 0 ⎟ ⎦ ⎝ θF ⎠ . * 315-316): 12
  14. 14. and the following bank’s value: β1 ⎧⎡ θ * 2 ⎤⎛ θ ⎞ ⎪⎢ F − I⎥⎜ * ⎟ ⎪ ⎣ 9δ (1 − ζ ) ⎦ ⎝ θ F ⎠ θ < θF * NPVF (θ F ;θ ) = ⎨ * if (23b) ⎪ θ2 θ ≥ θF * ⎪ −I ⎩ 9δ (1 − ζ ) Equation (23a) shows that the optimal entry threshold ( θ F ) has a reverse relation with * the intensity of network effect ζ ; while it has a positive relation with the uncertainty of network externality σ 2 (or δ ↓ ). Equation (23b) indicates that banks should invest when demand exceeds the investment threshold θ ≥ θ F ; otherwise, they should wait for * a better time to invest. Theorem 1 therefore could be derived here. Theorem 1: If the network externality is considered, the best investment threshold of a following bank is: 1 1 ⎧ β ⎫2 ⎧ β ⎫2 ∗ ⎣ ( ) θ F = 3 ⎨ 1 I δ (1 − ζ ) ⎬ = 3 ⎨ 1 I ⎡ λ − 2α − σ 2 (1 − ζ ) ⎤ ⎬ ⎦ ⎩ β1 − 2 ⎭ ⎩ β1 − 2 ⎭ From Theorem 1, we further can understand the investment factors of a following bank by the comparative static analysis. We concluded the results in Proposition 1. Proposition1:If there is consumer’s network effect in existence, the following bank’s optimal entry threshold will increase by the following factors: (1) higher fixed cost, I ; (2) higher demand uncertainty, σ 2 ; (3) lower average demand growth, α ; (4) higher risk-free interest rate, r ; and (5) lower network effect intensity, ζ . 13
  15. 15. 3.2 Leader’s Decision-Making 3.2.1 Decision-making in Stage 2 If there are no competitors in the market, Bank 1 enters the market and becomes the market leader with monopoly profits generated. However, other banks will be drawn to enter the market to compete when the profits are exceptionally high (demand threshold is θ ≥ θ F ). * When the leader is a monopolist, this leading bank’s value VL (θ ) must satisfy the following quadratic differential equation: 1 2 2 θ2 σ θ VL′′(θ ) + αθVL′ (θ ) − rVL (θ ) + =0 (24) 2 4 (1 − ζ ) In Equation (24), the first three items stand for the options value of the leaders that are waiting for the right time to enter the market; the last item of the equation stands for the fundamental value while the leading Bank 1 does not withdraw from the market and the following Bank 2 does not enter the market. The solution to the leading bank’s investment value function in Equation (24) is similar to the solution to the following bank’s investment value function in Equation (14): β1 β2 ⎡ θ2 ⎤ VL (θ ) = A1 ⋅ θ + A2 ⋅ θ +⎢ ⎥ (25) ⎣ 4δ (1 − ζ ) ⎦ When the demand falls, competitors will choose not to enter the market; thus, 14
  16. 16. A2 = 0 . Equation (25) can be simplified as follows: ⎡ θ2 ⎤ VL (θ ) = A1 ⋅θ β1 + ⎢ ⎥ (26) ⎣ 4δ (1 − ζ ) ⎦ If the demand goes up, competitors will be drawn to enter the market; therefore, a monopoly leading bank becomes a duopoly bank. Moreover, the leading bank’s value equals to the value function under Cournot-Nash competition. Therefore, the following value-matching condition must be substantiated: VL (θ F ) = V0F (θ F ) * * (27) We can solve A1 by applying Equation (27) and Equation (19) to Equation (25): −5θ F − β1 *2 A1 = (28) 36δ (1 − ζ ) Therefore, leading bank’s investment value function equals to: −5θ F − β1 β1 ⎡ θ 2 *2 ⎤ VL (θ ) = θ +⎢ ⎥ (29) 36δ (1 − ζ ) ⎣ 4δ (1 − ζ ) ⎦ Equation (29) indicates that under the monopoly market, the leading bank’s θ2 investment profit originally was . However, it has to be shared with the 4δ (1 − ζ ) potential competitors if the following banks eventually enter the market, and the profit 5θ 2 14 loss is . 36δ (1 − ζ ) We next analyze the adjustment of investment threshold for the leading banks at 14 Because the investment timing of the following bank is at θ ≥ θ F , the following bank will have its * investment postponed when θ < θF * ; therefore, θF = θ * in Equation (29). 15
  17. 17. stage 1 when facing potential competitors (the following banks). 3.2.2 Decision-making in Stage 1 When banks have decided to have investment plan executed at the time in which the demand threshold is θ L ≥ θ M ( θ M is the demand threshold under monopoly), the * deferral options value of investment is 15 β1 ⎡ β ⎡ θL 2 ⎤ ⎤⎛ θ ⎞ NPVL (θ L ;θ ) = ⎢ A1θ L 1 + ⎢ ⎥ − I⎥⎜ ⎟ ⎣ ⎣ 4δ (1 − ζ ) ⎦ ⎦ ⎝ θ L ⎠ β1 ⎧ −5θ F − β1 β1 ⎡ θ L ⎪ *2 2 ⎤ ⎫⎛ θ ⎞ ⎪ =⎨ θL + ⎢ ⎥ − I ⎬⎜ ⎟ (30) ⎩ 36δ (1 − ζ ) ⎪ ⎣ 4δ (1 − ζ ) ⎦ ⎭ ⎝ θ L ⎠ ⎪ θL 2 Two economic implications are in Equation (30). First, represents the 4δ (1 − ζ ) monopoly profits of the leader if there is not any threat from the potential competitors. 5θ F − β1 *2 β Second, θ L 1 represents the leader’s profits that have to be shared with the 36δ (1 − ζ ) following banks in market. When θ = θ F , the leading bank’s investment value function VL (θ F ) in Equation * ∗ θF 2 * (29) equals to − I . In addition, if the following banks choose to wait for the 9δ (1 − ζ ) right timing ( θ < θ F ), and the leading banks have investment made θ = θ L , Equation * * (23b) shows: 15 It is similar to the computation of the following bank’s deferral value for an investment at the demand threshold in the future; therefore, the calculation will not be processed here again. 16
  18. 18. β1 ⎡ θF 2 * ⎤⎛ θ ⎞ θF 2 * ⎢ − I⎥⎜ * ⎟ = −I ⎣ 9δ (1 − ζ ) ⎦ ⎝ θ F ⎠ θ =θ F * 9δ (1 − ζ ) that is, when θ = θ F , the leading bank’s value equals to the following bank’s value. * From Equation (30), the optimal demand investment threshold θ L of the leading ∗ bank if considering the deferral value of an investment maximized is: 1 1 ⎧ β ⎫2 ⎧ β ⎫2 θ L = 2 ⎨ 1 I ⎣δ (1 − ζ ) ⎦ ⎬ = 2 ⎨ 1 I ⎡( λ − 2α − σ 2 ) (1 − ζ ) ⎤ ⎬ * ⎡ ⎤ ⎣ ⎦ (31) ⎩ β1 − 2 ⎭ ⎩ β1 − 2 ⎭ Apparently, Equation (31) shows that the optimal entry threshold ( θ L ) will increase: * (1) when the intensity of network effect ( ζ ) decreases; (2) when the uncertainty of network externality σ 2 increase (or δ ↓ ). Thus, we can derive the Theorem 2 here. Theorem 2: If the network externality is considered, the best investment threshold of a leading bank is: 1 1 ⎧ β ⎫2 ⎧ β ⎫2 θ L = 2 ⎨ 1 I ⎣δ (1 − ζ ) ⎦ ⎬ = 2 ⎨ 1 I ⎡( λ − 2α − σ 2 ) (1 − ζ ) ⎤ ⎬ * ⎡ ⎤ ⎣ ⎦ ⎩ β1 − 2 ⎭ ⎩ β1 − 2 ⎭ Similarly, we also can observe the investment factors of a leading bank by the comparative static analysis. The results are concluded in Proposition 2. Proposition2. If there is consumer’s network effect in existence, the leading bank’s optimal entry threshold is same as the one in Theorem 1. However, the leading bank’s investment threshold is lower than the threshold of the following bank. 3.2.3 Economic Implications 17
  19. 19. Under the market without preemption and cost difference, and banks are with the features of demand uncertainty and network externality, banks have incentives to become a leading bank. While the entry threshold reaches θ F , following banks are ∗ encouraged to enter the market; therefore, the business performance is expected to go down. The role of leading bank and following bank is assumed to be exogenously given in this study; however, the influential factors to bank’s investment network platform are concluded in Theorem 1 and Theorem 2. 4. Demand Threshold and Bank’s Entry Equilibrium Strategy In the duopoly competition model above, there are two possible entry strategies: (1) sequential entry, and (2) simultaneous entry. The initial demand condition will affect the type of entry; thus, the first mover advantage could be described a phenomenon of path dependence 16 . According to Theorem (1) and (2), the intensity of network effect will influence the bank’s entry timing, thus the optimal investment timing strategy will be affected by the initial threshold value. That is, banks are with various equilibrium strategies. We then illustrate the bank’s equilibrium strategies in Figure 1. 16 According to conventional literatures, first mover advantage (FMA) origins from (1) economies of scale and learning effect, (2) programmed and converted cost, (3) network externality, and (4) quality uncertainty of consumer goods. However, empirical studies show that FMA could be different even in the same industry. Thus, Muller (1997) argued that the path dependence was the main factor of FMA. 18
  20. 20. 4.1 Sequential Entry Strategy Once the bank’s investment game starts, if θ ≤ θ F , the competitive banks will have * a symmetric sub-game perfect equilibrium strategy 17 . If the competitors have not yet entered the market, when θ L ≤ θ , one should enter the market immediately for * preemption. However, if the competitors are in market, a sequential entry strategy is the optimal strategy. In other words, when θ ≤ θ F , a second bank will enter the market and * become a following bank once the waiting entry threshold reaches θ F . * Under the above strategy, the oligopoly market equilibrium strategy is the leading bank will enter market immediately once the waiting timing is θ L ≤ θ . As for the * following bank at θ L , the deferral investment profit is no difference from the * investment profit due to VL (θ L ) = V0F (θ L ) . * * 4.2 Simultaneous Entry Strategy When the demand exceeds threshold value θ ≥ θ F , competitors will enter the * market simultaneously and with Cournot-Nash competition equilibrium reached. Therefore, we have Theorem 3 stated here. Theorem 3: 17 We considered only pure strategy for simplicity. Mixed strategy is to be studied in the future. 19
  21. 21. (1) When θ < θ L , both leading bank and following bank are waiting for the right * time to invest; (2) When θ L ≤ θ < θ F , leading bank is in market while the * * following bank is still waiting for the right time to invest; therefore, it is a sequential entry equilibrium strategy; (3) When θ > θ F , both leading bank and * following bank are in market; therefore, it is a simultaneous entry equilibrium strategy. 5. Analysis of Social Welfare According to the traditional economic theory, a monopoly market is with maximum deadweight loss, and the loss in an oligopoly market could be decreased by introducing market competition. However, under the Real Options Approach framework, irreversible investment is a sunk cost; therefore, waiting for an investment is with time value. Besides, banks with network externality have the economies of scale, resulting in a decrease of average cost. Added to it the uncertainty and network intensity, the claim of conventional theory about improving social welfare with competition should be further studied. In this section, the social welfare derived from different demand thresholds and parameters is used to validate the conclusion of generating higher social welfare from competition. 20
  22. 22. 5.1 Social Welfare under Different Demand Thresholds (1) When θ < θ L , both leading bank and following bank are waiting for the right time * to invest. The deferral value for an investment is equal to: ⎡ NPVL (θ L ,θ ) + NPVF (θ L , θ ) ⎤ ∗ ∗ ⎣ ⎦ β1 ⎧ θL *2 ⎫⎛ θ ⎞ ( ∗ ) where NPVL θ ,θ = NPVF (θ ;θ ) = ⎨ * − I ⎬⎜ ∗ ⎟ . ⎩ 9δ (1 − ζ ) ⎭⎝ θ L ⎠ L L Therefore, the social welfare equals to 18 β1 ⎧ θL *2 ⎫⎛ θ ⎞ 2⎨ − I ⎬ ⎜ ∗ ⎟ Pr θ < θ L . ∗ ( ) ⎩ 9δ (1 − ζ ) ⎭⎝ θ L ⎠ (2) When θ L ≤ θ < θ F , the leading bank is in market to invest while the following bank * * is still waiting for the right time to invest; therefore, it is a sequential entry equilibrium strategy. Under this equilibrium, the leading bank’s producer surplus θ2 (industry’s monopoly profits) equals to Vim = ; moreover, the following 4δ (1 − ζ ) β1 ⎡ θF 2 * ⎤⎛ θ ⎞ bank’s waiting investment value is NPVF (θ ;θ ) = ⎢ * − I ⎥ ⎜ * ⎟ ; also, ⎣ 9δ (1 − ζ ) ⎦ ⎝ θ F ⎠ F 18 Social welfare includes the deferral investment value and NPV of firms and consumer; therefore, the probability of first passage time, ( ) Pr θ < θ L , must be considered. According to Harrison (1985): * defining M T = Max ln θt , then t∈[ 0, T ] θ θ ⎛ ln θ i − μT ⎞ 2μ ⎛ − ln θ i − μT ⎞ Pr (θ ≤ θi ,τ > T ) = Pr ( M T ≤ ln θi ) = N ⎜ 0 ⎜ σ T ⎟− ⎟ ( ) θi σ 2 θ0 N⎜ ⎜ σ T 0 ⎟ , where ⎟ ⎝ ⎠ ⎝ ⎠ μ =α − 1σ2. 2 21
  23. 23. θ2 consumer surplus equals to CS m = . Thus, the social welfare at the time 8δ (1 − ζ ) equals to: ⎡CSm + Vim + NPVF (θ F ;θ ) ⎤ Pr (θ L ≤ θ ≤ θ F ) ⎣ * ⎦ ∗ ∗ β1 ⎡ 3θ 2 ⎡ θF 2 * ⎤⎛ θ ⎞ ⎤ =⎢ +⎢ − I ⎥ ⎜ * ⎟ ⎥ Pr (θ L ≤ θ ≤ θ F ) ∗ ∗ ⎢ 8δ (1 − ζ ) ⎣ 9δ (1 − ζ ) ⎦ ⎝ θ F ⎠ ⎥ ⎣ ⎦ β1 ⎡ 3θ 2 ⎡ θF 2 * ⎤⎛ θ ⎞ ⎤ =⎢ +⎢ − I ⎥ ⎜ * ⎟ ⎥ ⎡ Pr (θ ≤ θ F ) − Pr (θ ≤ θ L ) ⎤ . ∗ ∗ ⎢ 8δ (1 − ζ ) ⎣ 9δ (1 − ζ ) ⎦ ⎝ θ F ⎠ ⎥ ⎣ ⎦ ⎣ ⎦ (3) When θ ≥ θ F , both leading bank and following bank are in the market to invest; * therefore, it is a simultaneous entry strategy. Under this equilibrium, the bank’s producer surplus (industry’s profits) in the oligopoly market equals to ⎛ θ2 ⎞ 2θ 2 Vc = ⎜ ⎜ 9δ (1 − ζ ) ⎟ . Also, consumer surplus equals to CSc = 9δ (1 − ζ ) . Thus, the ⎟ ⎝ ⎠ social welfare equals to: ⎡ θ2 ⎤ [CSc + Vc ] Pr (θ ≥ θ F ) = ⎢ ∗ ⎥ ⎡1 − Pr (θ ≤ θ F ) ⎤ ∗ ⎣ 3δ (1 − ζ ) ⎦ ⎣ ⎦ The results are illustrated in Table 1. However, the magnitude of welfare effect in different stages cannot be identified in general. We therefore identify the change of social welfare effect based on different parameter specifications in the next section. 5.2 Sensitivity Analysis We assume that the demand of consumers’ banking service is with 1% annual 22
  24. 24. growth rate ( α = 0.01 ) and use the volatility ( σ = 0.2 ) to indicate the uncertainty of demand. Moreover, we assume risk-free interest rate (annum) is 12% ( r = 0.12 ) and the necessary return rate ( λ ) equals to 14%. Also, the project due date T is for 2-year, sunk cost is I = 1 , the intensity of network externality is ς = 0.3 , and initial demand is θ 0 = 0.75 . Table 2 shows the results of the sensitivity analysis depending on different parameter specifications. 5.2.1 Increase in demand uncertainty ( σ 2 ) When σ 2 is increased from 0.02 to 0.04 and 0.06, the waiting value of investment for banks goes up from 0.02 to 0.54 and 1.73, respectively. It implies that waiting for an investment is valuable. The social welfare is reduced from 2.24 to 2.11 first but increased to 2.49 later. The conclusion is in conformity with the conventional Real Options Approach, that is, competition does not necessarily help increase social welfare. 5.2.2 Increase in network externality intensity ( ς ) If ς is up from 0.3 to 0.4 and 0.5, the social welfare is increased from 2.11 to 3.15 and 4.94, respectively. On the other hand, social welfare is the highest when the network externality helps banks to be a monopolist. Therefore, greater network externality helps to reinforce the incentives for bank’s entry for advantages of 23
  25. 25. preemption. Furthermore, a monopoly bank is able to provide the market with all service demand without the help of following banks in order to avoid inefficiency of over-investment. 5.2.3 Increase in initial demand ( θ 0 ) When θ 0 goes up from 0.65 to 0.75 and 0.85, social welfare is increased from 0.99 to 2.10 and 4.01, respectively. Social welfare under monopoly will also go up along with the increase of initial demand. The result concluded that competition does not necessarily help generate social welfare under the uncertainty and network externality. 6. Conclusion It is demonstrated in the literature that network externality is a crucial factor to the bank’s profits and market share. Greater intensity of network effect and greater uncertainty of network externality help banks acquire greater profits than the marketing of non-Internet banks. Therefore, to improve profitability, banks must invest in network service platforms and aggressively promote network marketing before competitors enter the market. However, it takes a great deal of sunk cost and faces severe demand uncertainty for banks to have network transaction platforms constructed. Therefore, even with the 24
  26. 26. consumer’s network effect, the Real Options Approach suggests banks to await or to suspend investment temporarily and keep management flexible in order to increase bank’s value when: (1) sunk cost increases; (2) uncertainty of demand increases; (3) average growth rate of demand declines; and (4) risk-free interest rate goes up. In addition, the demand threshold determines bank’s equilibrium entry strategy, thus, it is important for banks to control the demand uncertainty with various marketing strategies. We also have different social welfare formulas calculated under different demand thresholds. By the sensitivity analysis, we concluded that competition does not necessarily help generate higher social welfare if: (1) demand uncertainty increases, (2) intensity of network externality increases, and (3) initial demand is higher. The result is different from the conclusion made under the conventional model in which competition helps improve social welfare. This is because the waiting value of an investment is emphasized under the Real Options Approach to avoid inefficiency of over-investment. In this study, we do not take into account the role of the government. When the market is with externality and deadweight loss, the government is suggested to implement policies to correct the inefficiency. Therefore, how and to what extent government intervention can improve social welfare under the Real Options Approach framework is the topic for future research. 25
  27. 27. Figure 1: The investment value of leading and following banks at different demand thresholds 26
  28. 28. Table 1: Social Welfare under Different Investment Thresholds θ < θL * θL ≤ θ < θF * * θ ≥ θF * Value of Standby β1 β1 ⎧ θL *2 ⎫⎛ θ ⎞ ⎡ θF 2 * ⎤⎛ θ ⎞ ⎨ − I ⎬⎜ ∗ ⎟ ⎢ − I⎥⎜ * ⎟ 0 Investment ⎩ 9δ (1 − ζ ) ⎭⎝ θ L ⎠ ⎣ 9δ (1 − ζ ) ⎦ ⎝ θ F ⎠ θ2 ⎛ θ2 ⎞ Vim = Vc = ⎜ Producer’s Surplus 0 4δ (1 − ζ ) ⎜ 9δ (1 − ζ ) ⎟ ⎟ ⎝ ⎠ θ2 2θ 2 Consumer’s Surplus 0 CSm = CSc = 8δ (1 − ζ ) 9δ (1 − ζ ) β1 ⎧ θL *2 ⎫⎛ θ ⎞ 2⎨ − I ⎬⎜ ∗ ⎟ Pr (θ < θ L ) ⎡ ∗ β1 9δ (1 − ζ ) ⎭⎝ θ L ⎠ 3θ 2 ⎡ θF 2 * ⎤⎛ θ ⎞ ⎤ ⎡ θ2 ⎤ Social Welfare ⎩ ⎢ +⎢ − I ⎥ ⎜ * ⎟ ⎥ Pr (θ L ≤ θ ≤ θ F ) ∗ ∗ ⎢ ⎥ ⎡1 − Pr (θ ≤ θ F ) ⎤ ∗ ⎢ 8δ (1 − ζ ) ⎣ 9δ (1 − ζ ) ⎦ ⎝ θ F ⎠ ⎥ ⎣ 3δ (1 − ζ ) ⎦ ⎣ ⎦ ⎣ ⎦ 27
  29. 29. Table 2: Results of Sensitivity Analysis θ < θL * θL ≤ θ < θF * * θ ≥ θF * Social Welfare σ 2 = 0.02 0.024663 2.180638 0.03974 2.245041 σ 2 = 0.04 0.54335 1.500783 0.061833 2.105966 σ 2 = 0.06 1.72548 0.732803 0.030011 2.488293 ς = 0.3 0.54335 1.500783 0.061833 2.105966 ς = 0.4 0.490633 2.515062 0.145923 3.151618 ς = 0.5 0.300926 4.27239 0.370097 4.943413 θ 0 = 0.65 0.495298 0.485809 0.010508 0.991615 θ 0 = 0.75 0.54335 1.500783 0.061833 2.105966 θ 0 = 0.85 0.411173 3.362309 0.241137 4.014619 28
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